Jacobi Zeta Function

Denoted zn(u,k) or Z(u).


where phi is the Jacobi amplitude, m is the parameter, and F(phi|m) and K(m) are elliptic integrals of the first kind, and E(m) is an elliptic integral of the second kind. See Gradshteyn and Ryzhik (2000, p. xxxi) for expressions in terms of theta functions. The Jacobi zeta functions is implemented in the Wolfram Language as JacobiZeta[phi, m].

See also

Elliptic Integral of the First Kind, Elliptic Integral of the Second Kind, Heuman Lambda Function, Zeta Function

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Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 595, 1972.Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press, 2000.Tölke, F. "Jacobische Zeta- und Heumansche Lambda-Funktionen." §132 in Praktische Funktionenlehre, dritter Band: Jacobische elliptische Funktionen, Legendresche elliptische Normalintegrale und spezielle Weierstraßsche Zeta- und Sigma Funktionen. Berlin: Springer-Verlag, pp. 94-99, 1967.

Referenced on Wolfram|Alpha

Jacobi Zeta Function

Cite this as:

Weisstein, Eric W. "Jacobi Zeta Function." From MathWorld--A Wolfram Web Resource.

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